Updated 3:38 p.m. | The leadership shuffle to succeed House Majority Leader Eric Cantor has begun, after the Virginia Republican suffered a shocking upset in a primary race Tuesday night. At least two representatives are already in the race to become the second-highest ranking member in the House.

Cantor will tell rank-and-file members his next steps at a 4 p.m. GOP conference meeting in the Capitol, and will address the press in a 4:30 p.m. (watch it live here) .

A source told CQ Roll Call that Cantor will announce he's stepping down from his leadership post on July 31 to give time for a transition to new leadership.

In a morning leadership meeting, Cantor did not tip his hand, according to a source in the room. But the race to succeed him, either in a special leadership election if he vacates the post or in the next Congress, is already well underway.

Already, sources say Majority Whip Kevin McCarthy, R-Calif., the third ranking Republican in the House, is the most prepared to step in to the position. Exiting a morning meeting, he declined to confirm that he will run. Sources close to him say he has wide support in the conference and is ready to make the move, and he is meeting with allies to discuss the race.

There is an appetite among conservative members for someone else, however, leaving open the opportunity someone more aligned with the Republican Study Committee and the tea party movement. One name sources speculate about is Financial Services Chairman Jeb Hensarling, R-Texas, and in a statement to CQ Roll Call he left the possibility open.

“I am humbled by the many people who have approached me about serving our Republican Conference in a different capacity in the future," he said. "There are many ways to advance the causes of freedom and free enterprise, and I am prayerfully considering the best way I can serve in those efforts." As Hensarling is deciding on his next steps, he is being spurred on by a cabal of conservative members who met for lunch Wednesday afternoon, including Rep. Mick Mulvaney. The South Carolina Republican said Hensarling is his dream candidate for the position because he is conservative and from the South.

"I do think there’s a difference between a red-state Republicans and a blue-state or purple-state Republican. The people you go home to are different, the language that's used is different," Mulvaney said.

Adding to that, a group of members from the Texas delegation was set to meet Wednesday afternoon to decide whom they would support. The delegation is the largest Republican bloc in the conference, and if the Lone Star State lawmakers vote together, they can be a formidable force.

When asked whether he would support someone from his home state, Rep. Michael C. Burgess, R-Texas, said, "I'm always for the Texan."

Sessions may also run for the majority whip post, if he finds the race against McCarthy futile — and especially if Hensarling enters the fray. But there is already a crowded field shaping up there. A source close to Chief Deputy Whip Peter Roskam, R-Ill., said he is still planning to seek out the whip slot in the 114th Congress. He had already been rounding up support in recent weeks, calling and meeting with members and donating money to campaigns. Republican Study Committee Chairman Steve Scalise, R-La., has made his intention to run for the slot known to colleagues as well.

Rep. Mo Brooks, R-Ala., said that neither McCarthy, Roskam, Scalise nor Sessions are conservative enough for his taste in a majority leader.

Though some conservative are pining for a red-state Republican to represent them at the leadership table, other moderate and blue-state Republicans said the current leadership team has done an effective job.

Rep. Pat Tiberi, R-Ohio, said he has not decided on whom to support, but he did say both McCarthy and Roskam are popular, despite coming from Democratic-leaning states.

"They both have a very successful tenure in their positions in leadership and they have a lot of support within the conference generally speaking for the job that they’ve done," he said.

Other members who seemed comfortable in their current roles just the day before were suddenly eying promotions.

Rep. Cathy McMorris Rodgers, R-Wash., announced, however, that she would stay put as conference chairwoman.

“After much encouragement from my colleagues, conversations with my family, and many prayers, I have decided to remain Conference Chair at this time," she said in a statement. "I look forward to continue leading my colleagues and building on our successes to introduce a culture of innovation to Capitol Hill, improve the image of House Republicans, and unite our entire Conference behind conservative solutions that serve people in every corner of America.”

A GOP aide familiar with McMorris Rodgers' thinking said she had been fielding calls from colleagues asking if she would want to move up to serve as whip or majority leader.

Conference Vice Chairwoman Lynn Jenkins, R-Kan., had eyed McMorris Rodgers' spot if it had been vacated, according to an aide.

Then there's the question of Speaker John A. Boehner of Ohio. Sources speculated that a leadership vacuum might make him more inclined than ever to stay on as speaker next Congress to avoid an all-out chaotic war to succeed him. On the other hand, there is always the chance he could decide to leave after this term.